Risk small trade size, let your profit run, cut your losses short. Even at a 50% win rate you'd still come out ahead in the game. Ah all of the sudden gambling is indeed VERY entertaining.

I've heard the cut your losses and let your winners run advice many times before and it has never made sense to me.

Are we saying:

(a) The performance of my trade on day 1 affects its performance on day 2? I.e. if I'm up today it makes a loss tomorrow more likely due to mean reversion or whatever. Or...

(b) Trade performances are independent of the past, like a coin toss or roulette wheel, but there is some behavior/algorithm that will increase the odds of winning repeated trials of a game beyond the underlying odds of the game. I.e. In a 50%/50% repeated coin toss game, if you are down 2 flips you can stop playing and then start a new coin toss game to reset the odds? 1

To me, neither possibility makes the slightest sense.

If A, what is the theoretical basis to expect mean reversion or consistent back and forth motion in things like currency exchange rates? Does some force hold their values within some range? Also, if we are referring to means, wouldn't "let your losses recover" be equally valid advice as "let your gains run"?

If B, and I decide to accept odds of x% in day 1, why would I not accept the same odds in day 2 (other than being broke)?

Suppose I take a position today. I then look back at how the position would have performed had I bought it yesterday and learn the position would have made money. Does that make it a mistake to have bought it today or an even better idea?